Individual Cracks Research Articles

The cellular transducer in damage-stimulated bone remodelling: a theoretical investigation using fracture mechanics

This paper reports on some theoretical work which used fracture mechanics concepts to draw conclusions about the nature of the so-called ‘cellular transducer’: the means by which bone cells detect the presence of damage and thus initiate remodelling and adaptation activities. Using analytical and numerical methods, we estimated the strains and displacements around cracks of the typical size, shape and orientation that normally occur in compact bone. We predicted that it is not possible for osteocytes or their processes to be fractured as a result of direct tensile strains, because the strains generated are much less than the expected failure strains of cellular material. We proposed a new failure mechanism by which osteocyte processes spanning the crack are cut by shearing motions between the crack faces. We predicted that failures of this type can occur. Failures begin to occur if crack lengths become greater than normal (100 μm), so this could act as a signal to initiate repair processes for individual cracks. Very large numbers of cell processes (greater than 1000) will fail if the crack length and/or applied stress reach dangerous levels (300 μm and 60 Mpa, respectively) at which point bone deposition may be required to prevent stress fractures. Similar results also occurred if we proposed a different mechanism of damage detection, involving cells’ ability to detect the high levels of strain that occur near crack tips. This work, though based on theoretical mechanics considerations, suggests some biological experiments which might confirm our findings.

Thermoelastic mechanism for logarithmic slow dynamics and memory in elastic wave interactions with individual cracks.

Logarithmic-in-time slow dynamics has been found for individual cracks in a solid. Furthermore, this phenomenon is observed during both the crack acoustic conditioning and the subsequent relaxation. A thermoelastic mechanism is suggested which relates the log-time behavior to the essentially 2D character of the heating and cooling of the crack perimeter and inner contacts. Nonlinear perturbation of the contacts by a stronger (pump) wave causes either softening or hardening of the sample, and induces either additional absorption or transparency for a weaker (probe) acoustic wave depending on frequency of the latter.

Ground Cracks Associated with the 1994 Double Spring Flat Earthquake, West-Central Nevada

The 1994 Double Spring Flat earthquake ( M W 5.8) occurred within a densely faulted step-over between the Genoa and Antelope Valley faults, two principal normal faults of the transition zone between the Basin and Range Province and the northern Sierra Nevada. The earthquake created zones of ground cracks from 0.1 to 2.8 km long along at least five northwest- to north-northwest-striking faults in the epicentral area. Individual cracks had extensional openings generally from 1 to 10 mm wide. No cracks displayed obvious vertical separation, and only one zone showed permissive evidence of right-lateral separation. Over the 8 days following the mainshock (the period over which the cracks were found), aftershocks formed a dominant northeast trend suggesting the earthquake occurred along a northeast-striking structure. However, no ground breakage was found along faults striking parallel to this northeast aftershock alignment, and subsequent aftershocks formed a conjugate northwest trend. Based on the location and character of the five zones, the observed cracks are attributed to secondary fault slip and shaking effects. The earthquake also created ground cracks along at least two faults 15-25 km from the epicenter. In both of these cases, the faults had documented histories of prior ground cracking, indicating that they are particularly susceptible to such triggered deformation. Manuscript received 21 August 2002.

Photon emission accompanying deformation and fracture of ice

We observed photon emission during deformation and fracture of axially loaded polycrystalline ice. Emission of visible photons (300–650 nm) was correlated with crack generation and fracture, based on time-resolved photon emission signals taken during load changes. Emission intensity, including the entire spectra ranging from 300 to 650 nm, was roughly correlated with increasing strain energy released by fracturing, while considerable scattering of the intensity data implied that emission intensity also depended on the characteristics of each individual crack. Correlation was taken between simultaneous emissions detected with two photomultiplier tubes with different ranges of spectral sensitivity. Brief, intense emissions were clearly associated with load drops, and these probably included wavelengths shorter than 320 nm, indicating that near ultraviolet light is also emitted. On the other hand, weak but continuous signals with wavelengths longer than 650 nm were emitted the entire time the ice was subjected to a load. Emission intensity and spectra may be attributed to microprocesses during fracturing. Experimental evidence for emission of visible photons indicates that the generated electric charges on crack surfaces and at crack tips have energy ranging from 2 to 6 eV. PACS No.: 46.50

Europa's dynamic icy crust

Abstract— Europa's icy crust records active resurfacing by tectonic and thermal processes over tens of millions of years, as rapidity demonstrated by a paucity of craters. Tidal working causes rotational torque, surface stress, internal heating, and orbital evolution, which can explain the formation of observed tectonic crack patterns, ridges, crustal displacement, and chaotic terrain by processes involving connections between the surface and the underlying ocean through cracks, melt sites, and occasional impacts. These processes were recent, and thus most likely continue today. The permeability of the crust allows exchange of materials, including oxidants and exogenic organics from the surface and endogenic substances from the ocean, such that a habitable biosphere might extend to within a few centimeters of the surface. Continual changes in environmental conditions in the ice crust, such as deactivation of individual cracks after thousands of years (due to non‐synchronous rotation) and crustal thawing (releasing any trapped organisms), could provide drivers for biological adaptation, as well as opportunity for evolution.

Finite Element Modelling Damage in Brittle Matrix Composites

A finite element model of the deformation and failure of brittle matrix composites during matrix cracking and delamination has been developed. The model is underpinned by the micro-mechanics developed by Aveston, Cooper and Kelly, represented through a damage mechanics approach, in which the effect of individual cracks and fibres is smeared into a continuum response. The model allows matrix micro-cracking, shear, and tensile delamination to be modelled by intersecting failure surfaces in stress space. Comparison of the predictions by the finite element model with experiments shows promise for the analysis of critical engineering structures and components.

Modelling of fatigue crack growth at the microstructural level

Since the 1960s we have used the stress intensity parameter K to characterise the growth of fatigue cracks. More recently it has been demonstrated experimentally that this parameter does not work for small cracks: these cracks tend to grow faster than would be predicted using linear elastic fracture mechanics, they show lower threshold values for growth, and the one-to-one relationship between growth rate and stress intensity range breaks down. One reason for this behaviour is that these cracks are of the same order of size as the microstructure––typically <10 grain diameters. Material homogeneity can no longer be assumed; the behaviour of an individual crack depends on the local microstructure. Two modifications are required to the modelling equations: (i) the use of statistical parameters to describe behaviour, and (ii) the introduction of parameters related to the microstructure. This paper reviews the state of the art and describes some recent work which applies the same concepts to a model of fatigue in bone. The introduction of short-crack growth relationships helps us to model damage development and understand the dynamic relationship between fatigue and repair in this living material.

TIDAL‐TECTONIC PROCESSES AND THEIR IMPLICATIONS FOR THE CHARACTER OF EUROPA'S ICY CRUST

Jupiter's satellite Europa is covered by an icy crust, likely overlying a deep, global liquid water ocean. The mutually dependent relationship between the orbit and tidal processes controls Europa's rotation, heating, and stress. Observations of the surface and investigation of tidal‐tectonic processes indicate that the dominant types of surface terrain have been created by frequent repeated exposure of an underlying ocean to the surface. Surface lineaments, including ubiquitous cycloidal (chains of arcs) features, are correlated with tidal stress patterns, demonstrating that they form by crustal cracking but only if a substantial ocean is present to give adequate tidal amplitude. Stratigraphy of tectonic features, combined with models of how and where they formed, demonstrates a moderate rate of nonsynchronous rotation. Tidal driving of strike‐slip displacement (in which surface areas shear passed one another) by daily (85 hours on Europa) tidal stresses suggests that cracks penetrate to a liquid layer. The characteristic ridge sets that cover tectonic terrain may be built by tidal pumping of fluid and slush to the surface on a daily basis. Widespread tectonic dilation creates new surface as material rises from below. In addition to those tectonic terrains, nearly half of the surface is chaotic terrain, with morphology and other characteristics indicative of melt‐through from below, consistent with the tectonic indications of thin ice and plausible tidal heating rates. Formation of both chaotic and tectonic terrains has continually resurfaced the satellite, while connecting the ocean to the surface. Surface colorants correlate with locations where ocean water reached the surface, such as along large‐scale ridge systems and around chaotic terrain. As a result of tides, liquid water may have bathed crustal cracks and surfaces with heat, transporting and mixing substances vertically. Such daily transported materials would include substances from the oceanic reservoir, oxidants, and fuels created at the surface, as well as any organisms and their chemical products. Thus a variety of habitable environments likely exist in the crust. Deactivation of individual cracks after thousands of years (due to the tidally driven nonsynchronous rotation) constrains processes like ridge building and strike‐slip displacement and would require any living organisms to adapt to such change.

Dynamics of anisotropic composite cantilevers weakened by multiple transverse open cracks

In this paper an exact solution methodology, based on Laplace transform technique enabling one to analyze the bending free vibration of cantilevered laminated composite beams weakened by multiple non-propagating part-through surface cracks is presented. Toward determining the local flexibility characteristics induced by the individual cracks, the concept of the massless rotational spring is applied. The governing equations of the composite beam with open cracks as used in this paper have been derived via Hamilton's variational principle in conjunction with Timoshenko's beam model. As a result, transverse shear and rotatory inertia effects are included in the model. The effects of various parameters such as the ply-angle, fiber volume fraction, crack number, position and depth on the beam free vibration are highlighted. The extensive numerical results show that the existence of multiple cracks in anisotropic composite beams affects the free vibration response in a more complex fashion than in the case of beam counterparts weakened by a single crack. It should be mentioned that to the best of the authors' knowledge, with the exception of the present study, the problem of free vibration of composite beams weakened by multiple open cracks was not yet investigated.

Identification of damage tolerance of Ti3SiC2 by hardness indentations and single edge notched beam test

The damage tolerance of Ti3SiC2 has been identified by Vickers indentations and single edge notched beam (SENB) testing. The Vickers indentations were made at loads of 0·5—30 kg to measure the hardness. The results showed that the hardness decreased with increasing loads. No indentation cracks were observed around the damage zones, even when the load applied was 30 kg. The material around microhardness indentations was pushed out, lots of grains were crushed into fragments under loads, and some grains exhibited lamination fracture. In addition, around the damage zones, a number of individual grains were delaminated and deformed heavily into a twisted shape. This suggests that Ti3SiC2 exhibits plasticity at room temperature. Moreover, the SENB test also suggested that this layered material is damage tolerant. The multi-absorbing energy mechanisms: grain pushout, pullout, and delamination, the buckling of individual grains, crack deflection, crack branching, and pinning, explained why the Ti3SiC2 is a damage tolerant material able to contain the extent of microdamage.

Initiation and early growth of fatigue cracks in an aerospace aluminium alloy

Abstract Material imperfections usually play a substantial role in the early stages of fatigue cracking. This article presents some observations concerning fatigue crack initiating flaws and early crack growth in 7050‐T7451 aluminium alloy specimens and in full‐scale fatigue test articles with a production surface finish. Equivalent initial flaw size (EIFS) approaches used to evaluate the fatigue implications of metallurgical, manufacturing and service‐induced features were refined by using quantitative fractography to acquire detailed information on the early crack growth behaviour of individual cracks; the crack growth observations were employed in a simple crack growth model developed for use in analysing service crack growth. The use of observed crack growth behaviour reduces the variability which is inherent in EIFS approaches which rely on modelling the whole of fatigue life, and which can dominate EIFS methods. The observations of realistic initial flaws also highlighted some of the significant factors in the fatigue life‐determining early fatigue growth phase, such as surface treatment processes. Although inclusions are often regarded as the single most common type of initiating flaw, processes which include etching can lead to etch pitting of grain boundaries with significant fatigue life implications.

Propagation of edge cracking towards the centre of laminated composite plates subjected to fatigue loading

The aim of this study is to propose and identify a model suitable for describing the damage distribution D( x, N), where x is the distance from an edge and N is the number of cycles, inside an off-axis layer of a laminate and to relate this internal damage with the surface damage D(0, N)= F( N) observable on the specimen's edge. The partial differential equation governing crack density D( x, N) is derived with the help of purely kinematical considerations on one hand and of the selected growth rate equation for each individual crack on the other, taking into account the mean crack spacing in the vicinity of the crack tip. A further aspect of the modelling, the relationship between crack density and strain energy release rate, is also investigated in the case of cross-ply laminates.

Characteristics of fatigue crack growth in GFRP laminates

Multiple fatigue crack growth behaviour has been studied in quasi-isotropic GFRP laminates under constant amplitude fatigue loading conditions. Characteristics of fatigue crack growth in off-axis plies have been described and comparisons have been made between quasi-static and fatigue crack growth behaviour. Careful monitoring of individual fatigue cracks reveals three distinct stages of crack growth including initiation, steady-state crack growth (SSCG) and crack interaction and saturation. Stress redistribution due to matrix cracking and the associated stiffness reduction have been simulated using finite element models. Strain energy release rates associated with the off-axis matrix cracking have also been obtained and correlated with the measured fatigue crack growth rates.

Contact based delamination and fracture analysis of composites

A new approach based on the concepts of the discrete element method, is presented for impact resistance analysis of composites. The method is capable of analysing the progressive fracturing and fragmentation behaviour, as well as potential post-cracking interactions caused by the newly created crack sides and segments. The imminence of a material crack is monitored by an anisotropic Hoffman model. To avoid the mesh dependency of the results, a bilinear local softening model, based on modes I and II, is also adopted in this study to account for release of energy and redistribution of forces that caused the formation of a crack. A special re-meshing method has been developed to geometrically model an individual crack by splitting the element, separating the failed node, creating new nodes and dividing the neighbouring elements to preserve the compatibility conditions. Numerical simulations have been performed to assess the performance of the proposed algorithm. The method has proved to be an efficient approach for impact analysis of composites undergoing progressive delamination and cracking.

Characterization of R-curve behavior in Si 3N 4-based ceramics

The exponential function proposed by Ramachandran and Shetty (J. Am. Ceram. Soc., 74 (1991) 2634–2641) was employed to describe the R-curves measured by directly observing the stable growth of annealed indentation cracks in the tensile surface of the specimen during bending test of four grades of Si 3N 4-based ceramics. It was shown that this exponential function gives a satisfactory description for the experimental data measured from each individual crack. A detailed explanation for the physical meanings of the adjustable parameters included in this function was then presented. Some useful parameters, including the critical crack resistance, the threshold crack resistance and the flaw tolerance, were also deduced based on the analysis of the experimental data.

Effects of Rock Damage on Seismic Waves Generated by Explosions

In studying the physical processes involved in the generation of seismic waves by explosions, it is important to understand what happens in the region of high stresses immediately surrounding the explosion. This paper examines one of the processes that takes place in this region, the growth of pre-existing cracks, which is described quantitatively as an increase in rock damage. An equivalent elastic method is used to approximate the stress field surrounding the explosion and a micro-mechanical model of damage is used to calculate the increase in damage. Simulations for a 1 kt explosion reveal that the region of increased damage can be quite large, up to ten times the cavity radius. The damage is initiated on a damage front that propagates outward behind the explosive stress wave with a velocity intermediate between that of P and S waves. Calculations suggest that the amount of increased damage is controlled primarily by the initial damage and the extent of the region of increased damage is controlled primarily by the initial crack radius. The motions that occur on individual cracks when damage increases are converted to seismic moment tensors which are then used to calculate secondary elastic waves which radiate into the far field. It is found that, while the contribution from an individual crack is small, the combined effect of many cracks in a large region of increased damage can generate secondary waves that are comparable in amplitude to the primary waves generated by the explosion. Provided that there is asymmetry in the damage pattern, this process is quite effective in generating S waves, thus providing a quantitative explanation of how S waves can be generated by an explosion. Two types of asymmetry are investigated, a shear pre-stress and a preferred orientation of cracks, and it is found that both produce similar effects.

Modelling the effects of texture on the statistics of stage I fatigue crack growth

Abstract A physically based model for the growth of short fatigue cracks through a local grain structure is presented. The growth rate is taken to be proportional to the cyclic plastic displacement at the crack tip, which is evaluated using an existing solution for the continuous distribution of dislocations ahead of the crack in a slip band that is blocked by a grain boundary. The effect of the local microstructure and texture are incorporated using orientation factors relating the applied far field stress to the shear stress which causes a grain to grain variation in the mode II loading of the crack tip. The orientation factor for each grain is established by assigning the crystallographic orientation of the grain using a probabilistic description of the overall texture of the polycrystal. The effects of idealized fibre (〈111〉 and 〈100〉), double fibre and random textures are examined. The growth rates of many individual cracks through different local microtextures were calculated within a Monte Carlo fr...

Modelling the effects of texture on the statistics of stage I fatigue crack growth

Abstract A physically based model for the growth of short fatigue cracks through a local grain structure is presented. The growth rate is taken to be proportional to the cyclic plastic displacement at the crack tip, which is evaluated using an existing solution for the continuous distribution of dislocations ahead of the crack in a slip band that is blocked by a grain boundary. The effect of the local microstructure and texture are incorporated using orientation factors relating the applied far field stress to the shear stress which causes a grain to grain variation in the mode II loading of the crack tip. The orientation factor for each grain is established by assigning the crystallographic orientation of the grain using a probabilistic description of the overall texture of the polycrystal. The effects of idealized fibre (〈111〉 and 〈100〉), double fibre and random textures are examined. The growth rates of many individual cracks through different local microtextures were calculated within a Monte Carlo framework. This allows the influence of texture on not only the average behaviour of the short cracks but also the statistical variation in the behaviour to be examined. Curves showing the probability of propagating cracks reaching a given crack length in a given number of cycles are shown.

Fractography of crack networks in thin layers

The subject of this article is detection and description of random networks of cracks on a material surface. Thin layers of (Ti,Al)N on a hardmetal (WC–6%Co) substrate were subjected to thermomechanical loads by laser irradiation. Cracks in the coating caused by this load were examined by scanning electron microscopy (SEM). A special method for automatical detection of cracks in SEM images of the surface is based on the application of edge detection and sequential testing of the course of individual cracks. The system of cracks is classified into branches with respect to passing or finishing in knots. To derive the characteristics of the network, a regression model of branches with user-specified maximum of represented curvature is suggested. As an example of the output, the distribution of the local crack direction conditional on the crack length is shown.

Characterisation and quantification of multiple crack growth during low cycle fatigue

The collective growth of multiple microcracks (or short cracks) during low cycle fatigue of polycrystalline Cu–30%Zn, 316L and Fe–26Cr–1Mo is investigated. Scanning electron microscopy is employed to study the evolution of surface microcrack populations, as well as the growth of individual cracks, on smooth specimens cyclically deformed at constant plastic strain amplitudes. The damage accumulation process is quantified by construction of so-called damage accumulation (DA) profiles, which reveal important information about crack growth mode, crack initiation rates, strain localisation and crack coalescence. In addition, experimentally measured microcrack growth is quantified in terms of general crack growth relations. The uniformity of these relations for different materials indicates that growth barriers dictate the main differences in fatigue microcrack growth.